52 citations · 786 across the 59 of their papers we have counts for
64 papers
Recovery of the rod cross section shape
Vladislav V. Kravchenko, Sergii M. Torba, Alexander O. Vatulyan
A direct method for solving the inverse problem of determining the shape of the cross section of a rod is proposed. The method is based on Neumann series of Bessel functions repres…
Synthesis of a quantum tree Weyl matrix
Sergei A. Avdonin, Kira V. Khmelnytskaya, Vladislav V. Kravchenko
A method for successive synthesis of a Weyl matrix (or Dirichlet-to-Neumann map) of an arbitrary quantum tree is proposed. It allows one, starting from one boundary edge, to comput…
Reconstruction techniques for complex potentials
Vladislav V. Kravchenko
An approach for solving a variety of inverse coefficient problems for the Sturm-Liouville equation -y''+q(x)y=λy with a complex valued potential q(x) is presented. It is based on N…
Reconstruction techniques for quantum trees
Sergei A. Avdonin, Kira V. Khmelnytskaya, Vladislav V. Kravchenko
The inverse problem of recovery of a potential on a quantum tree graph from Weyl's matrix given at a number of points is considered. A method for its numerical solution is proposed…
Schrödinger equation with finitely many -interactions: closed form, integral and series representations for solutions
Vladislav V. Kravchenko, Víctor A. Vicente-Benítez
A closed form solution for the one-dimensional Schrödinger equation with a finite number of -interactions \[ \mathbf{L}_{q,\mathfrak{I}_{N}}y:=-y^{\prime\prime}+\left( q(x)+\sum…
Recovery of a potential on a quantum star graph from Weyl's matrix
Sergei A. Avdonin, Kira V. Khmelnytskaya, Vladislav V. Kravchenko
The problem of recovery of a potential on a quantum star graph from Weyl's matrix given at a finite number of points is considered. A method for its approximate solution is propose…